How are a company’s profits related to its sales? Let’s examine data from 71 large U.S. corporations. All amounts are in millions of dollars.
a) Histograms of Profits and Sales and histograms of the logarithms of Profits and Sales are seen below. Why are the re-expressed data better for regression?

b) Here are the scatterplot and residuals plot for the regression of logarithm of Profits vs. log of Sales. Do you think this model is appropriate?

c) Here’s the regression analysis. Write the equation.

d) Use your equation to estimate profits earned by a company with sales of 2.5 billion dollars.

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# of Companies # of Companies 80 60 40 20 15 -1000 1500 4000 4000 6500 Profits 10 T 5 I 1.0 2.0 3.0 Log (profits) 4.0 # of Companies 50 40 30 20 10 # of Companies 15 10 5 The 0 15,000 30,000 45,000 Sales 2.2 4.2 Log (sales) 3.2